Global existence of classical solutions of Goursat problem for quasilinear hyperbolic systems with BV data (Q2875742)

The author studies the Goursat problem for first-order quasilinear hyperbolic systems in the angular domain \(t\geq 0\), \(x_1(t)\leq x\leq x_2(t)\), with \(x_i(t)\) being the characteristics. Each characteristic field is assumed to be degenerate. Global existence of a unique classical solution to the problem is proven under the assumption that the boundary values are \(C^1\) bounded but sufficiently small in the BV sense. An application to the global existence an uniqueness of classical solutions of the characteristic boundary value problem for the equation of time-like extremal surfaces in Minkowski space is discussed in detail.